Mathematics Colloquia and Seminars

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First talk: Topology and homotopy in partially ordered sets Monday July 29th, 11am-12pm (This should be appropriate for undergraduates) A finite poset P can be regarded as a topological space with finitely many points. The open sets are obtained by choosing an antichain of P and all the points below it. Conversely, any finite space is a poset. Under this identification order preserving maps coincide with continuous maps and the homotopies between maps of finite posets are easy to describe. We will present a simple and beautiful idea of R. Stong from 1966 which allows us to decide whether two finite posets have the same homotopy type.